Angle sensing using differential magnetic measurement and a back bias magnet

ABSTRACT

A magnetic field sensor includes a back bias magnet to generate a DC magnetic field. First and second magnetic field sensing elements of the magnetic field sensor are disposed proximate to at least one ferromagnetic surface of a ferromagnetic target object. The first and second magnetic field sensing elements generate first and second electronic signals, respectively, in response to first and second sensed magnetic fields corresponding to the DC magnetic field but influenced by the at least one ferromagnetic surface. The magnetic field sensor generates a difference signal that is a difference of amplitudes of the first and second electronic signals. The difference signal is indicative of a rotation measurement of an absolute relative rotation of the ferromagnetic target object and the magnetic field sensor about a rotation axis.

CROSS-REFERENCE TO RELATED APPLICATIONS

None.

STATEMENT REGARDING FEDERALLY SPONSORED RESEARCH OR DEVELOPMENT

None.

BACKGROUND

Magnetic field sensors generally include a magnetic field sensingelement and other electronic components. Magnetic field sensors providean electrical signal representative of a magnetic field sensed by themagnetic field sensing element. Various types of magnetic field sensingelements are known, including Hall Effect elements and magnetoresistanceelements.

Magnetic field sensors provide information about a sensed ferromagneticobject by sensing fluctuations of the sensed magnetic field. Somemagnetic field sensors include a fixed permanent magnet in a so-called“back bias” arrangement. Such magnetic field sensors sense fluctuationsof the magnetic field associated with the permanent magnet as an objectmoves within a magnetic field generated by the magnet. In the presenceof a moving ferromagnetic object, the magnetic field sensed by themagnetic field sensor varies in accordance with a shape or profile ofthe moving ferromagnetic object (a “target object”).

In automotive applications, a typical magnetic field sensor mightdetermine a rotation of a target object, for example, a camshaft in anengine, and provide information about the rotation of the target object(e.g., an angle of rotation, etc.) to an engine control processor.

However, some current solutions can require complex processing by themagnetic field sensor to be able to determine the information about therotation of the target object (e.g., an absolute angle of rotation,speed of rotation, direction of rotation, etc.). Such complex processingcan require more expensive components and additional developmentexpense. Some current solutions employ multiple magnetic field sensingelements or complexly shaped target objects, which also can increasecomplexity and cost. It would be desirable to provide a magnetic fieldsensor that can generate an output signal representative of an absoluterelative rotational angle of the magnetic field sensor and a proximatetarget object. Therefore, an improved magnetic field sensor and targetobject arrangement is needed.

SUMMARY

This Summary is provided to introduce a selection of concepts in asimplified form that are further described below in the DetailedDescription. This Summary is not intended to identify key or essentialfeatures or combinations of the claimed subject matter, nor is itintended to be used to limit the scope of the claimed subject matter.

One aspect provides a magnetic field sensor that includes a back biasmagnet to generate a DC magnetic field. First and second magnetic fieldsensing elements of the magnetic field sensor are disposed proximate toat least one ferromagnetic surface of a ferromagnetic target object. Thefirst and second magnetic field sensing elements generate first andsecond electronic signals, respectively, in response to first and secondsensed magnetic fields corresponding to the DC magnetic field butinfluenced by the at least one ferromagnetic surface. The magnetic fieldsensor generates a difference signal that is a difference of amplitudesof the first and second electronic signals. The difference signal isindicative of a rotation measurement of an absolute relative rotation ofthe ferromagnetic target object and the magnetic field sensor about arotation axis.

BRIEF DESCRIPTION OF THE DRAWING FIGURES

Other aspects, features, and advantages of the described embodimentswill become more fully apparent from the following detailed description,the appended claims, and the accompanying drawings in which likereference numerals identify similar or identical elements. Referencenumerals that are introduced in the specification in association with adrawing figure might be repeated in one or more subsequent figureswithout additional description in the specification in order to providecontext for other features.

FIG. 1A is a diagram showing an illustrative system having a magneticfield sensor with two magnetic field sensing elements proximate to atarget object with a helical groove;

FIG. 1B is a diagram showing another view of the target object of FIG.1A;

FIG. 2 is a side view of the target object and magnetic field sensor ofFIGS. 1A and 1B;

FIG. 3 is a schematic block diagram of an electronic circuit of themagnetic field sensor of the system of FIGS. 1A and 1B;

FIG. 4 is a graph showing plots of difference signals generated by themagnetic field sensor of FIGS. 1A and 1B, at two different air gapsbetween the magnetic field sensor and the target object, versus relativerotation of the target object of FIGS. 1A and 1B;

FIG. 5A is a diagram showing another illustrative system having amagnetic field sensor with two magnetic field sensing elements proximateto another target object with a different helical groove;

FIG. 5B is a diagram showing another illustrative system having amagnetic field sensor with two magnetic field sensing elements proximateto another target object with a helical ridge;

FIG. 6A is a graph showing plots of difference signals generated by themagnetic field sensor of FIG. 5A, at two different air gaps between themagnetic field sensor and the target object, versus relative rotation ofthe target object of FIG. 5A;

FIG. 6B is a graph showing plots of difference signals generated by themagnetic field sensor of FIG. 5B, at two different air gaps between themagnetic field sensor and the target object, versus relative rotation ofthe target object of FIG. 5B;

FIG. 7A is a diagram showing another illustrative system having amagnetic field sensor with two magnetic field sensing elements proximateto a target object with a another different helical groove;

FIG. 7B is a diagram showing another view of the target object of FIG.7A;

FIG. 8 is a graph showing plots of difference signals generated by themagnetic field sensor of FIG. 7A, at two different air gaps between themagnetic field sensor and the target object, versus relative rotation ofthe target object of FIG. 7A;

FIG. 9 is a diagram showing another illustrative system having amagnetic field sensor with two magnetic field sensing elements proximateto a target object with offset spiral segments;

FIG. 10 is a diagram showing a cross-sectional view of the target objectof FIG. 9;

FIG. 11 is a graph showing plots of difference signals generated by themagnetic field sensor of FIGS. 9 and 10, at two different air gapsbetween the magnetic field sensor and the target object, versus relativerotation of the target object of FIGS. 9 and 10;

FIG. 12 is a diagram showing another illustrative system having amagnetic field sensor with two magnetic field sensing elements proximateto a target object located at an end of a rotating shaft;

FIG. 13 is a graph showing a plot of a difference signal generated bythe magnetic field sensor of FIG. 12, versus relative rotation of thetarget object of FIG. 12;

FIG. 14 is a diagram showing another illustrative system having amagnetic field sensor proximate to a target object located at an end ofa rotating shaft; and

FIG. 15 is a diagram showing another illustrative system having amagnetic field sensor proximate to a target object located at an end ofa rotating shaft.

DETAILED DESCRIPTION

As used herein, the term “magnetic field sensing element” is used todescribe a variety of electronic elements that can sense a magneticfield. The magnetic field sensing element can be, but is not limited to,a Hall effect element, a magnetoresistance element, or amagnetotransistor. There are different types of Hall effect elements,for example, a planar Hall element, a vertical Hall element, and aCircular Vertical Hall (CVH) element. There are also different types ofmagnetoresistance elements, for example, a semiconductormagnetoresistance element such as Indium Antimonide (InSb), a giantmagnetoresistance (GMR) element, for example, a spin valve, ananisotropic magnetoresistance element (AMR), a tunnelingmagnetoresistance (TMR) element, and a magnetic tunnel junction (MTJ).The magnetic field sensing element might be a single element or,alternatively, might include two or more magnetic field sensing elementsarranged in various configurations, e.g., a half bridge or full(Wheatstone) bridge. Depending on the device type and other applicationrequirements, the magnetic field sensing element might be a device madeof a type IV semiconductor material such as Silicon (Si) or Germanium(Ge), or a type III-V semiconductor material like Gallium-Arsenide(GaAs) or an Indium compound, e.g., Indium-Antimonide (InSb).

Some of the above-described magnetic field sensing elements tend to havean axis of maximum sensitivity parallel to a substrate that supports themagnetic field sensing element, and others of the above-describedmagnetic field sensing elements tend to have an axis of maximumsensitivity perpendicular to a substrate that supports the magneticfield sensing element. In particular, planar Hall elements tend to haveaxes of sensitivity perpendicular to a substrate, while metal based ormetallic magnetoresistance elements (e.g., GMR, TMR, AMR) and verticalHall elements tend to have axes of sensitivity parallel to a substrate.

As used herein, the term “magnetic field sensor” is used to describe acircuit that uses a magnetic field sensing element, generally incombination with other circuits. Magnetic field sensors are used in avariety of applications, including, but not limited to, an angle sensorthat senses an angle of a direction of a magnetic field, a currentsensor that senses a magnetic field generated by a current carried by acurrent-carrying conductor, a magnetic switch that senses the proximityof a ferromagnetic object, a rotation detector that senses passingferromagnetic articles, for example, magnetic domains of a ring magnetor a ferromagnetic target (e.g., gear teeth) where the magnetic fieldsensor is used in combination with a back bias or other magnet, and amagnetic field sensor that senses a magnetic field density of a magneticfield.

As used herein below, the term “target object” is used to describe amechanical structure, movement of which is sensed by a magnetic fieldsensor.

As used herein, the term “groove” is used to describe a furrow orchannel, for example, in a target object. The groove forms an indent inan outer surface of the target object. The groove can circumscribe thetarget object, extending around or upon all of, or a portion of, theouter surface of the target object. The groove might be V-shaped withflat first and second surfaces that intersect at a sharp vertex.Alternatively, the surfaces of the groove might not be flat and/or thevertex might not be sharp, but might instead be rounded or flat.

As used herein, the term “ridge” is used to describe a raised region,for example, in a target object. The ridge might typically extend abovean outer surface of the target object. The ridge might circumscribe thetarget object, extending entirely around the target object, or mightextend only around or extend upon only a portion of the outer surface ofthe target object. The ridge might be V-shaped with flat first andsecond surfaces that intersect at a sharp vertex. Alternatively, thesurfaces of the ridge might not be flat and/or the vertex might not besharp, but might instead be rounded or flat.

As used herein, the term “movement axis” is used to describe an axisalong which a target object can move linearly relative to a location ofa magnetic field sensor. The term “movement axis” is also used todescribe an axis along which the magnetic field sensor can move linearlyrelative of a location of a ferromagnetic target object. In somearrangements, both the ferromagnetic target object and the magneticfield sensor can move relative to each other along respective movementaxes.

As used herein, the term “movement line” is used to describe a line,which might be straight or curved, along which a target object can moverelative to a location of a magnetic field sensor. The term “movementline” is also used to describe a line, straight or curved, along whichthe magnetic field sensor can move relative of a location of aferromagnetic target object. In some arrangements, both theferromagnetic target object and the magnetic field sensor can moverelative to each other along respective movement lines.

It should be understood that a movement line can be a movement axis anda movement axis can be a movement line. However, a movement line can becurved while a movement axis is straight.

As used herein, the term “rotation axis” is used to describe an axisupon which a target object can rotate or spin. In some arrangements, themovement axis and the rotation axis are parallel to each other. In somearrangements, the movement axis and the rotation axis are the same axis.In some embodiments described herein, a target object can spin about arotation axis and does not move along a movement line. In someembodiments described herein, a target object does not spin about arotation axis but can move along a movement line. In some embodimentsdescribed herein, a target object can both spin about a rotation axiscan move along a movement line.

Described embodiments measure an absolute relative angular position of arotating shaft relative to a magnetic field sensor over a rotation rangeup to one hundred eighty degrees in some embodiments and over a rotationarrange of three hundred sixty degrees in other embodiments. By“absolute relative angular position,” it is meant that one of or both ofa magnetic field sensor and a shaft can rotate about a rotation axis(e.g., a relative position), and that an absolute position of therelative rotation can be determined (e.g., forty-five degrees).Embodiments can be employed for end of shaft and side shaft measurement.As described below, a magnetic field sensor is made of two magneticfield sensing elements (e.g., Hall elements) that are few millimetersaway from each other and a back bias magnet. A target object made offerromagnetic material (e.g., steel) can be disposed proximate to themagnetic field sensor. An output of the magnetic field sensor can berelated to a difference of magnetic fields experienced by two Hallelements. Described embodiments provide specific target shapes thatcreate a monotonic differential field at the magnetic field sensorlocation.

Referring to FIG. 1A, a sensing system 100 includes magnetic fieldsensor 102 disposed proximate to ferromagnetic target object 104. Insome embodiments, magnetic field sensor 102 might include a back biasmagnet 102 c and two (or more) magnetic field sensing elements 102 a and102 b disposed between ferromagnetic target object 104 and the back biasmagnet 102 c. In some embodiments, a magnetization direction of themagnet (and a direction of the sensed magnetic field) is substantiallyalong the Z-axis as labelled in FIG. 1A.

Ferromagnetic target object 104 can include a helical groove 106 with agroove length 106 c and with groove surfaces 106 a and 106 bintersecting at vertex 106 e. As indicated by a flat region 106 d, thehelical groove 106 can extends only part way around a ferromagnetictarget object 104, for example, one hundred eighty degrees around theferromagnetic target object 104, and a back side behind the helicalgrove 106 can be, for example, flat.

As described in greater detail below in regard to FIG. 3, an outputsignal from magnetic field sensor 102 is representative of an absoluterelative angle of ferromagnetic target object 104 relative to magneticfield sensor 102 in a direction about axis 108. In some embodiments,ferromagnetic target object 104 is operable to rotate or spin aboutrotation axis 108, as indicated by line 112.

Referring to FIG. 1B, helical groove 106 extends only part way aroundferromagnetic target object 104, for example, less than three hundredsixty degrees around the ferromagnetic target object 104, and a backside behind the helical grove 106 can be, for example, flat section 106d. As shown in FIG. 1A, flat section 106 d has a width 106 f that allowssensing system 100 to determine an absolute relative rotation of lessthan three hundred sixty degrees of ferromagnetic target object 104. Insome embodiments, width 106 f might be approximately ten degrees, suchthat sensing system 100 can determine an absolute relative rotation ofthree hundred fifty degrees of ferromagnetic target object 104.

Referring to FIG. 2, in which like elements of FIGS. 1A and 1B are shownhaving like reference designations, ferromagnetic target object 104 andmagnetic field sensor 102 are separated by air gap 202. As describedbelow, a dimension of air gap 202 is related to a magnitude of magneticfields sensed by the magnetic field sensor 102. The air gap 202 is usedin graphs below.

Referring to FIG. 3, an illustrative electronic circuit 300 can bedisposed upon a substrate in magnetic field sensor 102. Electroniccircuit 300 might include or be coupled to one or more magnetic fieldsensing elements (shown in FIG. 3 as magnetic field sensing elements 302a and 302 b), which might be the same as or similar to the magneticfield sensing elements in each of the magnetic field sensors describedherein.

Magnetic field sensing elements 302 a and 302 b experience a magneticfield (e.g., 301) in a back bias arrangement over groove 106 (e.g., asin magnetic field sensor 102 shown in FIGS. 1 and 2). The magnetic field(e.g., 301) generated by the back bias magnet 102 c is influenced by theferromagnetic target object 104. As ferromagnetic target object 104rotates about rotation axis 108, a distance between magnetic fieldsensing elements 302 a and 302 b and helical groove 106 changes indifferent ways, resulting in magnetic field sensing elements 302 a and302 b experiencing different magnitudes of magnetic fields asferromagnetic target object 104 rotates.

Signals 303 a and 303 b from magnetic field sensing elements 302 a and302 b, respectively, can be received by a differential amplifier 304. Insome embodiments, adjustments might be made to operating parameters ofdifferential amplifier 304 during a calibration period of electroniccircuit 300. For example, differential amplifier 304 might include inputrange and coarse sensitivity adjustments.

Differential amplifier 304 generates difference signal 305, which mightbe received by coarse offset voltage adjustment circuit 306. Coarseoffset adjustment circuit 306 can generate an offset adjusted signal,for example, such that an offset adjusted signal is within anoperational range of N-bit analog-to-digital (A/D) converter 308. A/Dconverter 308, for example, a 14-bit A/D, can be coupled to receive theoffset corrected signal and can generate a digital signal. The digitalsignal can be received by signal processor 310. Signal processor 310might include a bandwidth and temperature compensation module 312.Bandwidth and temperature compensation module 312 might filter (e.g.,with a selectable bandwidth) and temperature compensate the offsetcorrected signal. Signal processor 310 might also include sensitivityand fine offset adjustment module 314 that provides a fine sensitivityand offset adjustment.

In some embodiments, signal processor 310 might also includelinearization module 316 coupled to sensitivity and fine offsetadjustment module 314. Linearization module 316 might generate alinearized output signal with respect to absolute relative rotationbetween ferromagnetic target object 104 and electronic circuit 300.Signal processor 310 might also include a clamping module 318 coupled toreceive the linearized output signal and to generate a clamped outputsignal. The clamped output signal might be a version of the linearizedoutput signal restricted to a particular range of values. In someembodiments, electronic circuit 300 does not include linearizationmodule 316, and instead, clamping module 318 couples to upstreamcircuits directly.

For embodiments in which magnetic field sensing elements 302 a and 302 bare Hall effect elements, electronic circuit 300 might include circuitry(not shown) to chop (or current spin) the Hall effect elements. Currentspinning is a known circuit technique that can result in lower apparentoffset voltages of Hall elements 302 a and 302 b.

Output format module 324 receives the clamped signal, and pulse widthmodulation (PWM) current modulator 320 can generate output signal 326proportional to values of the clamped signal. In some embodiments,output signal 326 has a duty cycle proportional to values of the clampedsignal. In some embodiments, output signal 326 is a current signalcarried on a common wire with a supply voltage that powers electroniccircuit 300.

In some embodiments, certain ranges of duty cycle of the PWM outputsignal 326 are used for other purposes. For example, duty cycles fromzero to ten percent and duty cycles from ninety to one hundred percentmight be used to signal fault conditions of electronic circuit 300.Thus, in some embodiments, clamping module 318 restricts values ofclamped signal to those values that would generate duty cycles in arange from about ten to about ninety percent. However, other duty cycleranges might alternatively be used.

To that end, electronic circuit 300 might include fault detector module322 that can provide a fault signal to output format module 324. Asshown, fault detector/diagnostics module 322 is coupled to the output ofdifferential amplifier 304 and detects invalid levels of the differencesignal 305. In other embodiments, fault detector/diagnostics module 322might be coupled to other signals of electronic circuit 300 and mightdetect other types of error conditions. More generally, faultdetector/diagnostics module 322 might monitor signal path validity andcommunicate fault condition(s) to the output. This is particularlyimportant for automotive safety related applications requiringconformity to Automotive Safety Integrity Level (ASIL).

While output format module 324 is described to generate a PWM outputsignal, in other embodiments, output signal 326 might be generated inaccordance with other formats, for example, a Single Edge NibbleTransmission (SENT) format, a Serial Peripheral Interface (SPI) format,a Local Interconnect Network (LIN) format, a CAN (Controller AreaNetwork) format, an Inter-Integrated Circuit (I2C) format, or othersimilar signal formats. For example, in automotive applications, outputsignal 326 might be communicated to an Electronic/Engine Control Unit(ECU) or Engine Control Module (ECM) or similar controller of anautomotive system.

Referring to FIG. 4, graph 400 has a horizontal axis with a scale inunits of degrees indicative of absolute relative rotation of a targetobject (e.g., target object 104) and a magnetic field sensor (e.g.,magnetic field sensor 102 of FIGS. 1A and 1B, coupled to electroniccircuit 300). Graph 400 has a vertical axis with a scale in units of themagnetic field (e.g., Gauss) sensed by the magnetic field sensor 102.Curves 402 and 404 are representative of difference signal 305 for twodifferent air gaps (see air gap 202 of FIG. 2). For example, curve 402is representative of the difference signal 305 for a 1 mm air gap (e.g.,air gap 202 of FIG. 2) between the magnetic field sensor 102 and thetarget object 104 of FIGS. 1A and 1B. Curve 404 is representative ofdifference signal 305 for a 2 mm air gap (e.g., air gap 202 of FIG. 2)between the magnetic field sensor 102 and the target object 104 of FIGS.1A and 1B.

It will be understood that linearity of the curves 402 and 404 can beinfluenced by a variety of circuits and factors. For example, thelinearity can be affected by the shape of target object 104 (e.g.,helical groove 106) and the signal processing performed by linearizationmodule 316 of FIG. 3. In some embodiments, linearization is controlledby the shape of target object 104 (e.g., helical groove 106 in targetobject 104), and the linearization module 316 is not needed.

Thus, as shown in FIGS. 1-4, described embodiments employ a back biasmagnet (e.g., 102 c of FIGS. 1A and 1B) within or adjacent to a magneticfield sensor (e.g., 102) having two Hall sensing elements 102 a and 102b that, for a stationary magnetic field sensor 102, measure a magneticfield in a direction along the Z-axis as shown in FIGS. 1 and 2. The twoHall sensing elements 102 a and 102 b are typically a few millimetersaway from each other along the X-axis as shown in FIGS. 1 and 2. Eachone of the magnetic field sensing elements 102 a and 102 b outputs arespective signal representative of a magnetic field experienced by eachmagnetic field sensing element. For example, magnetic field sensingelement 302 a outputs signal 303 a, and sensing element 302 b outputssignal 303 b. The magnetic field sensor output signal 326 isrepresentative of a difference (i.e., a differential arrangement) of thetwo signals (e.g., signal 303 b minus signal 303 a) performed by thedifferential amplifier 304.

The magnetic field sensor (e.g., 102 of FIGS. 1A and 1B), measures anabsolute relative rotational position of a ferromagnetic target object(e.g., 104), e.g., a shaft, by either a side shaft measurement such asshown in FIGS. 1A and 1B, or by an end of shaft measurement such asdescribed below in regard to FIG. 12. The ferromagnetic target object ismade of a ferromagnetic material (e.g., steel) in order to influence amagnetic field generated by the back bias magnet (e.g., 102 c of FIGS.1A and 1B).

To detect the shaft position, described embodiments of the shaft have atarget area (e.g., groove 106 with length 106 c) proximate to magneticfield sensor 102. The target area has a specific shape (e.g., a helicalgroove) to create a monotonic differential field at magnetic fieldsensor 102 as the relative rotation changes. To detect an absoluteposition of the shaft, the differential field is beneficially unique forany rotational position of the shaft. Further, the differential fieldcan be as linear as possible as the relative rotation changes to improvemeasurement accuracy and reduce post-processing requirements of signalprocessor 310.

In particular, the embodiment of shaft 104 shown in FIGS. 1A and 1B isbeneficially employed in a side shaft absolute relative measurementarrangement. As shown in FIGS. 1A and 1B, the target area employs aV-shaped helical groove 106. In some embodiments, helical groove 106might be similar to the threads of a screw. When shaft 104 rotates aboutthe X-axis (e.g., as indicated by line 112), each of the magnetic fieldsensing elements 102 a and 102 b experience a varying distance to asurface of the helical groove 106 with opposite direction. As the shaftrotates, if magnetic field sensing element 102 a experiences anincreasing air gap, then magnetic field sensing element 102 bexperiences a decreasing air gap (and vice versa). Consequently, thedifferential field is monotonic and symmetric as shaft 104 rotates, asshown in FIG. 4.

To have a monotonic differential field, described embodiments can meetthe following relationships:

$\begin{matrix}{{L > {3{S(1)}\mspace{14mu} {and}\mspace{14mu} P} < \frac{180L}{\theta}},} & (2)\end{matrix}$

where L is a length of the V-shape groove (e.g., dimension 106 c ofFIGS. 1A and 1B), S is a spacing between magnetic field sensing elements102 a and 102 b, θ is a maximum rotation range (in degrees), and P is ascrew pitch of helical groove 106. Curves 402 and 404 of FIG. 4represent signals generated by magnetic field sensor 102 (e.g.,difference signal 305 of FIG. 3) having two different air gaps (e.g.,air gap 202 having dimensions of 1 mm for curve 404 and 2 mm for curve404), which are shown in FIG. 4 for a +/−ninety degree rotation. Asshown in FIG. 4, curves 402 and 404 are monotonic and exhibit highlinearity over at least +/−ninety degrees (i.e., over a range of onehundred eighty degrees).

It should be understood that the magnetic field sensor 102 of the shaft104 of FIGS. 1A and 1B can be at different positions (or move) in the xdirection and still achieve the results of FIG. 4, so long as themagnetic field sensing elements 102 a and 102 b remain over the groove106. This is due to the differential arrangement provided by the twomagnetic field sensing elements 102 a and 102 b in combination withdifferential amplifier 304. In particular, the shape of groove 106 issuch that the distance between magnetic field sensing element 102 a andgroove surface 106 a is increasing while the distance between magneticfield sensing element 102 b and groove surface 106 b is decreasing, andvice versa.

Other shapes of target object 104 and helical groove 106 might improvelinearity of the sensed magnetic field (e.g., difference signal 305 ofFIG. 3) over a rotation of a target object. For example, it is possibleto improve or otherwise change the linearity by employing a roundedV-shape as shown in FIG. 5A or a ridge-shape as shown in FIG. 5B.

As shown in FIG. 5A, a sensing system 500 includes magnetic field sensor502 disposed proximate to ferromagnetic target object 504. In someembodiments, magnetic field sensor 502 might include a back bias magnet502 c and two (or more) magnetic field sensing elements 502 a and 502 bdisposed between ferromagnetic target object 504 and the back biasmagnet 502 c.

Ferromagnetic target object 504 can include a helical groove 506 with agroove length 506 c and with surfaces 506 a and 506 b intersecting at avertex 506 e. As indicated by a flat region 506 d, the helical groove506 extends only part way around the ferromagnetic target object 504,for example, less than three hundred sixty degrees around theferromagnetic target object 504, and a back side behind the helicalgrove 506 can be, for example, flat.

The shaft 504 has a rounded helical groove 506 where a slope of thesurfaces 506 a, 506 b are curved as shown. The better linearity is shownin FIG. 6A, where the magnetic field sensor 502, for both a 1 mm air gap(e.g., curve 604) and a 2 mm air gap (e.g., curve 602) exhibits improvedlinearity over a shaft having a straight V-shape (e.g., curves 404 and402 of FIG. 4).

As shown in FIG. 5B, a sensing system 530 includes magnetic field sensor532 disposed proximate to ferromagnetic target object 534. In someembodiments, magnetic field sensor 532 might include a back bias magnet532 c and two (or more) magnetic field sensing elements 532 a and 532 bdisposed between ferromagnetic target object 534 and the back biasmagnet 532 c.

Ferromagnetic target object 534 can include a helical ridge 536 with aridge length 536 c and with surfaces 536 a and 536 b intersecting at avertex 536 e. As indicated by a flat region 536 d, the helical ridge 536extends only part way around the ferromagnetic target object 534, forexample, less than three hundred sixty degrees around the ferromagnetictarget object 534, and a back side behind the helical ridge 536 can be,for example, flat.

The shaft 534 has the helical ridge 536 where a slope of the surface 536a is curved as shown. FIG. 6B shows the differential magnetic fieldsensed by magnetic field sensor 532, for both a 1 mm air gap (e.g.,curve 614) and a 2 mm air gap (e.g., curve 612), which exhibitsreasonable linearity in comparison to shafts having a helical groove(e.g., curves 404 and 402 of FIG. 4, and curves 604 and 602 of FIG. 6A,for example).

It should be noted that described embodiments above, for which helicalgroves (or ridges) do not extend all the way around respective shafts,it is not possible to measure rotation through a range of three hundredsixty degrees. To achieve measurements over rotations of up to andbeyond three hundred sixty degrees, the differential field experiencedby the magnetic field sensor (e.g., magnetic field sensor 502) needs tobe periodic, symmetric and monotonic over a rotation of one hundredeighty degrees.

FIG. 7A shows a sensing system 700 that includes magnetic field sensor702 disposed proximate to ferromagnetic target object 704. In someembodiments, magnetic field sensor 702 might include a back bias magnet702 c and two (or more) magnetic field sensing elements 702 a and 702 bdisposed between ferromagnetic target object 704 and the back biasmagnet 702 c.

Ferromagnetic target object 704 can include a helical groove 706 with agroove length 706 c and with surfaces 706 a and 706 b. Unlike thehelical grooves 106 and 506 above, the helical groove 706 extends allthe way around a shaft 704, in two conjoined groove portions. Only oneconjoined groove portion is shown and another conjoined portion isbehind the view shown.

Thus, an illustrative shaft 704 has a screw type helical groove 706having a first symmetric groove portion 710 a and a second symmetricgroove portion 710 b, which is in the back and not shown in detail.Thus, shaft 704 exhibits symmetry over two rotational ranges, zerodegrees to one hundred eighty degrees and one hundred eighty degrees tothree hundred sixty degrees.

FIG. 7B shows another view of sensing system 700. As shown in FIG. 7B,ferromagnetic target object 704 includes helical groove 706 withsurfaces 706 a and 706 b. Helical groove 706 extends all the way aroundshaft 704, in two symmetric conjoined groove portions, 710 a and 710 b,which are conjoined at seam 710 c. Thus, helical groove 706 and, thus,shaft 704, exhibits symmetry over two rotational ranges, zero degrees toone hundred eighty degrees and one hundred eighty degrees to threehundred sixty degrees (e.g., over portions 710 a and 710 b, separated byseam 710 c).

FIG. 8 shows curve 804 representative of the difference signal 305 for a1 mm air gap (e.g., air gap 202 of FIG. 2) between the magnetic fieldsensor 702 and the target object 704 of FIG. 7A. Curve 802 isrepresentative of difference signal 305 for a 2 mm air gap (e.g., airgap 202 of FIG. 2) between the magnetic field sensor 702 and the targetobject 704 of FIG. 7A. As shown, the signals exhibit symmetry about onehundred eighty degrees.

Assuming that an initial position of shaft 704 is known (e.g., whethergroove portion 710 a or 710 b is facing magnetic field sensor 702), itis possible to measure the absolute position of shaft 704 by detectingtransitions between groove portions (e.g., 710 a and 710 b). If theinitial position of shaft 704 is not known (e.g., it is not known whichof groove portions 710 a or 710 b are initially facing magnetic fieldsensor 702), then the position of shaft 704 is known relative to a+/−one hundred eighty degree shift. Detecting transitions between grooveportions 710 a and 710 b could be done, for example, by a peak detectormodule (not shown) of electronic circuit 300. Further, the absoluteposition detection does not require a rotation direction change of theshaft.

For example, a function θ gives the position within one of the onehundred eighty degree groove portions 710 a and 710 b as a function ofthe differential field AB experienced by magnetic field sensor 702 overrotation of the groove portions 710 a and 710 b (e.g., the portions ofcurves 802 and 804 from zero degrees to one hundred eighty degrees inFIG. 8). Then the absolute position, θ_(abs), of the shaft is given byθ_(abs)=θ(ΔB) in the groove portion representing zero degrees to onehundred eighty degrees, and by θ_(abs)=360°−θ(ΔB) in the groove portionrepresenting one hundred eighty degrees to three hundred sixty degrees.

In some embodiments, the magnetic field sensor is twisted around theZ-axis at an angle between zero degrees and ninety degrees (not shown).However, such a twisted sensor might have reduced measurement rangeversus a non-twisted sensor.

Referring to FIG. 9, a sensing system 900 includes magnetic field sensor902 having two magnetic field sensing elements 902 a and 902 b disposedproximate to ferromagnetic target object 904 for side shaft measurement.In some embodiments, magnetic field sensor 902 is proximate to (orincludes) back bias magnet 902 c. The ferromagnetic target object 904can have two segments 906 a and 906 b, each having a radius that changesin a direction around a rotation axis 908. One magnetic field sensingelement 902 a is aligned with shaft segment 906 a and another magneticfield sensing element 902 b is aligned with shaft segment 906 b. Each ofshaft segments 906 a and 906 b has a different shape (e.g., radius)based on a decreasing spiral such that, as the ferromagnetic targetobject 904 turns, one magnetic field sensing element 902 a has adecreasing distance to shaft segment 906 a while the other magneticfield sensing element 902 b has an increasing distance to the shaftsegment 906 b. Such embodiments can employ a target area 906 having anoverall length 906 c that is smaller than a comparable length of ahelical groove shown in embodiments above.

FIG. 10, in which elements of FIG. 9 are shown having like referencedesignations, shows a cross-sectional view of shaft 904 of FIG. 9 takenat the interface between segments 904 b and 906 b, as indicated by line905. As shown in FIG. 10, each of shaft segments 906 a and 906 b has adifferent shape (e.g., radius) based on a decreasing spiral such thatthe distance for one magnetic field sensing element is decreasing whilethe distance for the other magnetic field sensing element is increasing.

Referring now to FIG. 11, as shown by curves 1102 and 1104, the magneticfield sensor 902 of FIG. 9 can generate the difference signal 305 thatexhibits good linearity over a at least a +/−ninety degree rotation(i.e., over a range of at least one hundred eighty degrees).

The principles described above in regard to side-shaft measurement canalso be applied to end-of-shaft measurements of absolute rotationposition using specific target shapes described below.

Referring now to FIG. 12, sensing system 1200 for end-of-shaftmeasurements includes magnetic field sensor 1202 having two magneticfield sensing elements 1202 a and 1202 b and a back bias magnet 1202 c.Magnetic field sensor 1202 is disposed proximate to ferromagnetic targetobject 1204 (e.g., a rotating shaft having a target area 1206 located atthe end of the shaft). As shown in FIG. 12, target area 1206 includes aplurality of target segments 1206 (shown as target segments 1206 a, 1206b and 1206 c, although other numbers of segments might be employed). Asindicated by line 1212, shaft 1204 rotates about rotation axis 1208.Magnetic field sensing elements 1202 a and 1202 b sense rotation offerromagnetic target object 1204 as the sensed magnetic field changeswith respect to the shape of target segments 1206 a, 1206 b and 1206 c.For example, as shown in FIG. 12, target segments 1206 a, 1206 b and1206 c each have a starting width (1214 a, 1214 b and 1214 c,respectively) and taper to a point at the distal end of target area 1206(e.g., point 1216). Each of target segments 1206 a, 1206 b and 1206 chave a slope of the taper to point 1216. In some embodiments, each oftarget segments 1206 a, 1206 b and 1206 c might have a different widthand slope of the tapers to ease detection of each segment by magneticfield sensing elements 1202 a and 1202 b.

FIG. 13 shows curves representative of signals that can be generated bythe magnetic field sensor 1202 over a one hundred eighty degree rotationof shaft 1204. As shown by curve 1302, symmetry of target segments 1206a-1206 c allows the magnetic field sensor 1202 to exhibit linearity overat least one hundred eighty degree rotation of shaft 1204.

For end shaft and side shaft measurement, the sensed magnetic field canbe linear if the target is correctly designed. Described designs of thetarget provide improved linearity of the output of the magnetic fieldsensor that reduce, or ideally eliminate, the need for post-processing(e.g., by signal processor 310) to linearize the output. Further,described embodiments do not require complex integrated 2D/3D magneticfield measurement devices, zero gauss magnets or magnets of complexshapes.

Referring now to FIG. 14, sensing system 1400 for end-of-shaftmeasurements includes ferromagnetic target object 1404 (e.g., a rotatingshaft) having a target area 1406 located at the end of the shaft.Cross-sectional views are shown respective to line A-B and line C-D. Asshown in FIG. 14, target area 1406 includes target segments (or tracks)1406 a and 1406 b. A magnetic field sensor has magnetic field sensors(e.g., 1402 a and 1402 b) aligned over the target tracks to senserotation of ferromagnetic target object 1404. The sensed differentialmagnetic field changes with respect to the distance between magneticfield sensing elements 1402 a and 1402 b and target tracks 1406 a and1406 b.

To achieve good linearity, each of target tracks 1406 a and 1406 b has avariable slope that changes in a direction around a rotation axis. Insome embodiments, target tracks 1406 a and 1406 b are of oppositeslopes. For example, each of target tracks 1406 a and 1406 b has adifferent slope such that, as ferromagnetic target object 1404 turns,one magnetic field sensing element 1402 a has a decreasing distance totarget track 1406 a (and decreasing slope of the target track) while theother magnetic field sensing element 1402 b has an increasing distanceto target track 1406 b (and increasing slope of the target track), untilthe ends of the tracks are reached, for example at seam 1406 f.

FIG. 15, in which elements of FIG. 14 are shown having like referencedesignations, shows a cross-sectional view of an alternative embodimentof shaft 1404 of FIG. 14 having only a single target track 1406 a.Sectional views are shown respective to line A-B and line C-D. As shownin FIG. 14, magnetic field sensing elements 1402 a and 1402 b aredisposed over separate locations of target track 1406 a. In someembodiments, target track 1406 a has a different slope (e.g., a slopegradient) such that as the distance between the magnetic field sensingelements 1402 a and 1402 b and the target track is decreasing, the slopeof the target track is also decreasing, and that the change in slopeallows a difference signal to be detected between the magnetic fieldssensed by magnetic field sensing elements 1402 a and 1402 b. Otherembodiments might have a constant slope as the sensed magnetic field hasa decreasing slope, which has a gradient. Target track 1406 a ends atseam 1406 f Magnetic field sensing elements 1402 a and 1402 b arealigned over single target track 1406 a with a determined distanceseparating the two magnetic field sensing elements 1402 a and 1402 b.

Described embodiments are fully differential and employ back biasmagnets and ferromagnetic targets. In some embodiments, the magnet canbe integrated in the package with the magnetic field sensor. Describedembodiments have no upper limit for the sensed magnetic field level.

Reference herein to “one embodiment” or “an embodiment” means that aparticular feature, structure, or characteristic described in connectionwith the embodiment can be included in at least one embodiment of theclaimed subject matter. The appearances of the phrase “in oneembodiment” in various places in the specification are not necessarilyall referring to the same embodiment, nor are separate or alternativeembodiments necessarily mutually exclusive of other embodiments. Thesame applies to the term “implementation.”

As used in this application, the words “exemplary” and “illustrative”are used herein to mean serving as an example, instance, orillustration. Any aspect or design described herein as “exemplary” or“illustrative” is not necessarily to be construed as preferred oradvantageous over other aspects or designs. Rather, use of the words“exemplary” and “illustrative” is intended to present concepts in aconcrete fashion.

Additionally, the term “or” is intended to mean an inclusive “or” ratherthan an exclusive “or”. That is, unless specified otherwise, or clearfrom context, “X employs A or B” is intended to mean any of the naturalinclusive permutations. That is, if X employs A; X employs B; or Xemploys both A and B, then “X employs A or B” is satisfied under any ofthe foregoing instances. In addition, the articles “a” and “an” as usedin this application and the appended claims should generally beconstrued to mean “one or more” unless specified otherwise or clear fromcontext to be directed to a singular form.

To the extent directional terms are used in the specification and claims(e.g., upper, lower, parallel, perpendicular, etc.), these terms aremerely intended to assist in describing the embodiments and are notintended to limit the claims in any way. Such terms, do not requireexactness (e.g., exact perpendicularity or exact parallelism, etc.), butinstead it is intended that normal tolerances and ranges apply.Similarly, unless explicitly stated otherwise, each numerical value andrange should be interpreted as being approximate as if the word “about”,“substantially” or “approximately” preceded the value of the value orrange.

Also for purposes of this description, the terms “couple,” “coupling,”“coupled,” “connect,” “connecting,” or “connected” refer to any mannerknown in the art or later developed in which energy is allowed to betransferred between two or more elements, and the interposition of oneor more additional elements is contemplated, although not required.Conversely, the terms “directly coupled,” “directly connected,” etc.,imply the absence of such additional elements. Signals and correspondingnodes or ports might be referred to by the same name and areinterchangeable for purposes here.

As used herein in reference to an element and a standard, the term“compatible” means that the element communicates with other elements ina manner wholly or partially specified by the standard, and would berecognized by other elements as sufficiently capable of communicatingwith the other elements in the manner specified by the standard. Thecompatible element does not need to operate internally in a mannerspecified by the standard.

As used herein, the term “predetermined,” when referring to a value orsignal, is used to refer to a value or signal that is set, or fixed, inthe factory at the time of manufacture, or by external means, e.g.,programming, thereafter. As used herein, the term “determined,” whenreferring to a value or signal, is used to refer to a value or signalthat is identified by a circuit during operation, after manufacture.

Moreover, the terms “system,” “component,” “module,” “interface,”,“model” or the like are generally intended to refer to acomputer-related entity, either hardware, a combination of hardware andsoftware, software, or software in execution. For example, a componentmight be, but is not limited to being, a process running on a processor,a processor, an object, an executable, a thread of execution, a program,and/or a computer. By way of illustration, both an application runningon a controller and the controller can be a component. One or morecomponents might reside within a process and/or thread of execution anda component might be localized on one computer and/or distributedbetween two or more computers.

As used herein, the term “processor” is used to describe an electroniccircuit that performs a function, an operation, or a sequence ofoperations. The function, operation, or sequence of operations can behard coded into the electronic circuit or soft coded by way ofinstructions held in a memory device. A “processor” can perform thefunction, operation, or sequence of operations using digital values orusing analog signals.

In some embodiments, the “processor” can be embodied in an applicationspecific integrated circuit (ASIC). In some embodiments, the “processor”can be embodied in a microprocessor with associated program memory. Insome embodiments, the “processor” can be embodied in a discreteelectronic circuit. The “processor” can be analog, digital ormixed-signal.

While the illustrative embodiments have been described with respect toprocesses of circuits, described embodiments might be implemented as asingle integrated circuit, a multi-chip module, a single card, or amulti-card circuit pack. Further, as would be apparent to one skilled inthe art, various functions of circuit elements might also be implementedas processing blocks in a software program. Such software might beemployed in, for example, a digital signal processor, micro-controller,or general purpose computer.

Some embodiments might be implemented in the form of methods andapparatuses for practicing those methods. Described embodiments mightalso be implemented in the form of program code embodied in tangiblemedia, such as magnetic recording media, hard drives, floppy diskettes,magnetic tape media, optical recording media, compact discs (CDs),digital versatile discs (DVDs), solid state memory, hybrid magnetic andsolid state memory, or any other machine-readable storage medium,wherein, when the program code is loaded into and executed by a machine,such as a computer, the machine becomes an apparatus for practicing theclaimed invention. Described embodiments might also be implemented inthe form of program code, for example, whether stored in a storagemedium, loaded into and/or executed by a machine, or transmitted oversome transmission medium or carrier, such as over electrical wiring orcabling, through fiber optics, or via electromagnetic radiation,wherein, when the program code is loaded into and executed by a machine,such as a computer, the machine becomes an apparatus for practicing theclaimed invention. When implemented on a processing device, the programcode segments combine with the processor to provide a unique device thatoperates analogously to specific logic circuits. Such processing devicesmight include, for example, a general purpose microprocessor, a digitalsignal processor (DSP), a reduced instruction set computer (RISC), acomplex instruction set computer (CISC), an application specificintegrated circuit (ASIC), a field programmable gate array (FPGA), aprogrammable logic array (PLA), a microcontroller, an embeddedcontroller, a multi-core processor, and/or others, includingcombinations of the above. Described embodiments might also beimplemented in the form of a bitstream or other sequence of signalvalues electrically or optically transmitted through a medium, storedmagnetic-field variations in a magnetic recording medium, etc.,generated using a method and/or an apparatus as recited in the claims.

It should be understood that the steps of the illustrative methods setforth herein are not necessarily required to be performed in the orderdescribed, and the order of the steps of such methods should beunderstood to be merely examples. Likewise, additional steps might beincluded in such methods, and certain steps might be omitted orcombined, in methods consistent with various embodiments.

It will be further understood that various changes in the details,materials, and arrangements of the parts that have been described andillustrated herein might be made by those skilled in the art withoutdeparting from the scope of the following claims.

We claim:
 1. A magnetic field sensor, comprising: a back bias magnetconfigured to generate a DC magnetic field; first and second magneticfield sensing elements disposed along a sensing element line anddisposed proximate to at least one ferromagnetic surface of aferromagnetic target object, the first and second magnetic field sensingelements configured to generate first and second electronic signals,respectively, in response to first and second sensed magnetic fieldscorresponding to the DC magnetic field but influenced by the at leastone ferromagnetic surface; wherein the magnetic field sensor is operableto generate a difference signal that is a difference of amplitudes ofthe first and second electronic signals, and the difference signal isindicative of a rotation measurement of an absolute relative rotation ofthe ferromagnetic target object and the magnetic field sensor about arotation axis, wherein the sensing element line is substantiallyparallel to the rotation axis.
 2. The magnetic field sensor of claim 1,wherein the at least one ferromagnetic surface of the ferromagnetictarget object comprises a helical groove disposed on the ferromagnetictarget object, the helical groove configured to provide the differencesignal with respect to the absolute relative rotation.
 3. The magneticfield sensor of claim 2, wherein the difference signal is substantiallylinear with respect to the absolute relative rotation of theferromagnetic target object and the magnetic field sensor about therotation axis.
 4. The magnetic field sensor of claim 2, wherein the atleast one ferromagnetic surface comprises a first groove surface and asecond groove surface, the first and second groove surfaces intersectingat a vertex, thereby forming a V-shaped helical groove.
 5. The magneticfield sensor of claim 4, wherein the first groove surface and the secondgroove surface are straight in one dimension.
 6. The magnetic fieldsensor of claim 4, wherein the first groove surface and the secondgroove surface are curved in two dimensions.
 7. The magnetic fieldsensor of claim 6, wherein curvatures of the first and second groovesurfaces are selected to provide the difference signal as substantiallylinear with respect to the absolute relative rotation of theferromagnetic target object and the magnetic field sensor about therotation axis.
 8. The magnetic field sensor of claim 1, wherein theabsolute relative rotation of the ferromagnetic target object and themagnetic field sensor about the rotation axis comprises a rotation ofthe ferromagnetic target object about the rotation axis and the magneticfield sensor is stationary.
 9. The magnetic field sensor of claim 1,further comprising: a differential amplifier coupled to receive thefirst and second electronic signals and configured to generate thedifference signal.
 10. The magnetic field sensor of claim 1, wherein theferromagnetic target object comprises a rotating shaft, and the firstand second magnetic field sensing elements are disposed in a side-shaftmeasurement arrangement with respect to the rotating shaft.
 11. Themagnetic field sensor of claim 1, wherein the ferromagnetic targetobject is disposed at a distal end of a rotating shaft, and the firstand second magnetic field sensing elements are disposed in anend-of-shaft measurement arrangement with respect to the rotating shaft.12. The magnetic field sensor of claim 11, wherein the at least oneferromagnetic surface of the ferromagnetic target object comprises aplurality of target segments, each one of the plurality of targetsegments having a respective taper to a distal end of the rotatingshaft.
 13. The magnetic field sensor of claim 1, wherein theferromagnetic target object comprises a helical groove comprising ahelix structure having a first helix portion corresponding to anabsolute relative rotation of the ferromagnetic target object and themagnetic field sensor between zero degrees and a maximum rotation anglethat is less than three hundred sixty degrees, and a second portionproximate to the helical groove that is flat.
 14. The magnetic fieldsensor of claim 1, wherein the ferromagnetic target object comprises ahelical groove comprising a symmetrical helix structure having a firsthelix portion and a second helix portion, the first helix portioncorresponding to an absolute relative rotation of the ferromagnetictarget object and the magnetic field sensor between zero degrees and onehundred eighty degrees, and the second helix portion corresponding to anabsolute relative rotation of the ferromagnetic target object and themagnetic field sensor between one hundred eighty degrees and threehundred sixty degrees, wherein the first and second helix portions aresymmetrical with each other.
 15. The magnetic field sensor of claim 14,wherein the magnetic field sensor is configured to detect a one hundredeighty degree symmetry of the helix structure in regard to the absoluterelative rotation of the ferromagnetic target object and the magneticfield sensor, thereby determining an absolute relative rotation angleover a rotation greater than three hundred sixty degrees.
 16. Themagnetic field sensor of claim 15, wherein the absolute relativerotation angle, θ_(abs), of the ferromagnetic target object isdetermined by a relationship θ_(abs)=θ(ΔB) in the first helix portionand by the relationship θ_(abs)=360°−θ(ΔB) in the second helix portion,wherein θ(ΔB) is a differential of a magnetic field related to thedifference signal, wherein an amplitude of the difference signal isrelated to the absolute relative rotation of the ferromagnetic targetobject and the magnetic field sensor about the rotation axis.
 17. Themagnetic field sensor of claim 1, wherein the at least one ferromagneticsurface of the ferromagnetic target object comprises a first surfacehaving a first radius and a second surface having a second differentradius, the first and second surfaces disposed on the ferromagnetictarget object, the second surface displaced from the first surface in adirection along the rotation axis.
 18. The magnetic field sensor ofclaim 17, wherein the first and second surfaces are configured toprovide the difference signal that is substantially linear with respectto the absolute relative rotation of the ferromagnetic target object andthe magnetic field sensor about the rotation axis.
 19. The magneticfield sensor of claim 17, wherein the first magnetic field sensingelement is aligned with the first surface and the second magnetic fieldsensing element is aligned with the second surface, wherein the magneticfield sensor comprises a differential amplifier coupled to receive thefirst and second electronic signals and configured to generate thedifference signal as the difference between the amplitudes of the firstand second electronic signals, wherein an amplitude of the differencesignal is related to the absolute relative rotation of the ferromagnetictarget object and the magnetic field sensor about the rotation axis. 20.The magnetic field sensor of claim 17, wherein the first radius and thesecond radius have respective decreasing spirals, wherein a firstdistance between the first surface and the first magnetic field sensingelement decreases while a second distance between the second surface andthe second magnetic field sensing element increases in response tochanges of the absolute relative rotation of the ferromagnetic targetobject and the magnetic field sensor.
 21. The magnetic field sensor ofclaim 17, wherein the first radius and the second radius are selected toprovide the difference signal that is substantially linear with respectto the rotation of the ferromagnetic target object about the rotationaxis.
 22. The magnetic field sensor of claim 1, wherein theferromagnetic target object is disposed at a distal end of a rotatingshaft, the ferromagnetic target object comprising a first track and asecond track disposed about the rotation axis of the rotating shaft, thefirst track having a first slope and the second track having a secondslope; and wherein the first and second magnetic field sensing elementsare disposed in an end-of-shaft measurement arrangement with respect tothe rotating shaft, the first magnetic field sensing element is alignedwith the first track and the second magnetic field sensing elementaligned with the second track.
 23. The magnetic field sensor of claim 1,wherein the ferromagnetic target object is disposed at a distal end of arotating shaft, the ferromagnetic target object comprising a trackdisposed about the rotation axis of the rotating shaft, the track havinga slope; and wherein the first and second magnetic field sensingelements are disposed in an end-of-shaft measurement arrangement withrespect to the rotating shaft, the first magnetic field sensing elementis disposed over a first position of the track and the second magneticfield sensing element is disposed over a second position of the track.24. The magnetic field sensor of claim 23, wherein the slope isnon-linear.
 25. A method of sensing an absolute relative rotation of aferromagnetic target object and a magnetic field sensor about a rotationaxis, the method comprising: generating a DC magnetic field by a backbias magnet; generating first and second electronic signals,respectively, by first and second magnetic field sensing elementsdisposed along a sensing element line and disposed proximate to at leastone ferromagnetic surface of a ferromagnetic target object, the firstand second electronic signals in response to first and second sensedmagnetic fields corresponding to the DC magnetic field but influenced bythe at least one ferromagnetic surface; generating, by the magneticfield sensor, a difference signal that is a difference of amplitudes ofthe first and second electronic signals, and the difference signal isindicative of a rotation measurement of an absolute relative rotation ofthe ferromagnetic target object and the magnetic field sensor about arotation axis, wherein the sensing element line is substantiallyparallel to the rotation axis.
 26. The method of claim 25, comprising:providing the difference signal with respect to the absolute relativerotation by a helical groove disposed on at least one ferromagneticsurface of the ferromagnetic target object.
 27. The method of claim 26,wherein the difference signal is substantially linear with respect tothe absolute relative rotation of the ferromagnetic target object andthe magnetic field sensor about the rotation axis.
 28. The method ofclaim 26, wherein the at least one ferromagnetic surface comprises afirst groove surface and a second groove surface, the first and secondgroove surfaces intersecting at a vertex, thereby forming a V-shapedhelical groove.
 29. The method of claim 28, wherein the first groovesurface and the second groove surface are straight in one dimension. 30.The method of claim 28, wherein the first groove surface and the secondgroove surface are curved in two dimensions.
 31. The method of claim 30,comprising: providing the difference signal as substantially linear withrespect to the absolute relative rotation of the ferromagnetic targetobject and the magnetic field sensor about the rotation axis based uponcurvatures of the first and second groove surfaces.
 32. The method ofclaim 25, wherein the absolute relative rotation of the ferromagnetictarget object and the magnetic field sensor about the rotation axiscomprises a rotation of the ferromagnetic target object about therotation axis and the magnetic field sensor is stationary.
 33. Themethod of claim 25, further comprising: receiving, by a differentialamplifier, the first and second electronic signals and generating thedifference signal.
 34. The method of claim 25, wherein the ferromagnetictarget object comprises a rotating shaft, and the first and secondmagnetic field sensing elements are disposed in a side-shaft measurementarrangement with respect to the rotating shaft.
 35. The method of claim25, wherein the ferromagnetic target object is disposed at a distal endof a rotating shaft, and the first and second magnetic field sensingelements are disposed in an end-of-shaft measurement arrangement withrespect to the rotating shaft.
 36. The method of claim 35, wherein theat least one ferromagnetic surface of the ferromagnetic target objectcomprises a plurality of target segments, each one of the plurality oftarget segments having a respective taper to a distal end of therotating shaft.
 37. The method of claim 25, wherein the ferromagnetictarget object comprises a helical groove comprising a helix structurehaving a first helix portion corresponding to an absolute relativerotation of the ferromagnetic target object and the magnetic fieldsensor between zero degrees and a maximum rotation angle that is lessthan three hundred sixty degrees, and a second portion proximate to thehelical groove that is flat.
 38. The method of claim 25, wherein theferromagnetic target object comprises a helical groove comprising asymmetrical helix structure having a first helix portion and a secondhelix portion, the first helix portion corresponding to an absoluterelative rotation of the ferromagnetic target object and the magneticfield sensor between zero degrees and one hundred eighty degrees, andthe second helix portion corresponding to an absolute relative rotationof the ferromagnetic target object and the magnetic field sensor betweenone hundred eighty degrees and three hundred sixty degrees, wherein thefirst and second helix portions are symmetrical with each other.
 39. Themethod of claim 38, comprising: detecting, by the magnetic field sensor,a one hundred eighty degree symmetry of the helix structure in regard tothe absolute relative rotation of the ferromagnetic target object andthe magnetic field sensor; and determining an absolute relative rotationangle over a rotation greater than three hundred sixty degrees.
 40. Themethod of claim 39, comprising: determining the absolute relativerotation angle, θ_(abs), of the ferromagnetic target object by arelationship θ_(abs)=θ(ΔB) in the first helix portion and by therelationship θ_(abs)=360°−θ(ΔB) in the second helix portion, whereinθ(ΔB) is a differential of a magnetic field related to the differencesignal, wherein an amplitude of the difference signal is related to theabsolute relative rotation of the ferromagnetic target object and themagnetic field sensor about the rotation axis.
 41. The method of claim25, wherein the at least one ferromagnetic surface of the ferromagnetictarget object comprises a first surface having a first radius and asecond surface having a second different radius, the first and secondsurfaces disposed on the ferromagnetic target object, the second surfacedisplaced from the first surface in a direction along the rotation axis.42. The method of claim 41, comprising: providing the difference signalthat is substantially linear with respect to the absolute relativerotation of the ferromagnetic target object and the magnetic fieldsensor about the rotation axis based upon the first and second surfaces.43. The method of claim 41, comprising: aligning the first magneticfield sensing element with the first surface and aligning the secondmagnetic field sensing element with the second surface; receiving, by adifferential amplifier of the magnetic field sensor, the first andsecond electronic signals; and generating the difference signal as thedifference between the amplitudes of the first and second electronicsignals, wherein an amplitude of the difference signal is related to theabsolute relative rotation of the ferromagnetic target object and themagnetic field sensor about the rotation axis.
 44. The method of claim41, wherein the first radius and the second radius have respectivedecreasing spirals, wherein a first distance between the first surfaceand the first magnetic field sensing element decreases while a seconddistance between the second surface and the second magnetic fieldsensing element increases in response to changes of the absoluterelative rotation of the ferromagnetic target object and the magneticfield sensor.
 45. The method of claim 41, comprising: providing thedifference signal that is substantially linear with respect to therotation of the ferromagnetic target object about the rotation axisbased upon the first radius and the second radius.
 46. The method ofclaim 25, wherein the ferromagnetic target object is disposed at adistal end of a rotating shaft, the ferromagnetic target objectcomprising a first track and a second track disposed about the rotationaxis of the rotating shaft, the first track having a first slope and thesecond track having a second slope; and wherein the first and secondmagnetic field sensing elements are disposed in an end-of-shaftmeasurement arrangement with respect to the rotating shaft, the firstmagnetic field sensing element is aligned with the first track and thesecond magnetic field sensing element aligned with the second track. 47.The method of claim 25, wherein the ferromagnetic target object isdisposed at a distal end of a rotating shaft, the ferromagnetic targetobject comprising a track disposed about the rotation axis of therotating shaft, the track having a slope; and wherein the first andsecond magnetic field sensing elements are disposed in an end-of-shaftmeasurement arrangement with respect to the rotating shaft, the firstmagnetic field sensing element is disposed over a first position of thetrack and the second magnetic field sensing element is disposed over asecond position of the track.
 48. The method of claim 47, wherein theslope is non-linear.